The sides played out a goalless stalemate at the KC Stadium, with neither team looking likely to break the deadlock.
Tom Huddlestone tested Villa shot-stopper Brad Guzan on the brink of half-time but there was little else to speak of up front for the Tigers.
Having registered back-to-back wins in previous weeks, Bruce conceded his regret at not taking three points on home soil this weekend.
"We are disappointed because we have played particularly well over the last few weeks," he said.
"Still, against a really good Aston Villa team we stuck at it and for me it had a 0-0 draw written all over from the minute we kicked off.
"But, we will take it and move on."
With a two-week international break ahead, Bruce's men sit comfortably in mid-table - unbeaten at home - a position the Tigers boss is pleased with after the predictions of relegation struggles.
"We have to be delighted going into the [international] break, we have played four games at home, won two and drawn two," he added.
"There is a long winter ahead but we have made a good start. We didn't play very well today but we've got something from the game and we move on.
"We have to work on it, we are a newly-promoted team, one thing you have to be is thoroughly well organised.
"We did that remarkably well today and that is what earned us the point at the end of the day."
With Robbie Brady injured for Saturday's clash, Danny Graham was left to lead the Hull attack and with his goal drought now extended to 24 games, Bruce admitted his stocks are being stretched.
"You are only as good as your strikers and we don't have the resources to go out and buy a 20-goal-a-season man," he said.
"We have to do the best we can with the resources we have."